Robust group compressive sensing for DOA estimation with partially distorted observations

In this paper, we propose a robust direction-of-arrival (DOA) estimation algorithm based on group sparse reconstruction algorithm utilizing signals observed at multiple frequencies. The group sparse reconstruction scheme for DOA estimation is solved through the complex multitask Bayesian compressive sensing algorithm by exploiting the group sparse property of the received multi-frequency signals. Then, we propose a robust reconstruction algorithm in the presence of distorted signals. In particular, we consider a problem where the observed data in some frequencies are distorted due to, e.g., interference contamination. In this case, the residual error will follow the impulsive Gaussian mixture distribution instead of the Gaussian distribution due to the fact that some of the estimation errors significantly depart from the mean value of the estimation error distribution. Thus, the minimum least square restriction used in the conventional sparse reconstruction algorithm may lead to a failed reconstruction result. By exploiting the maximum correntropy criterion which is inherently insensitive to the impulsive noise, a weighting vector is derived to automatically mitigate the effect of the distorted narrowband signals, and a robust group compressive sensing approach is developed to achieve reliable DOA estimation. The robustness and effectiveness of the proposed algorithm are verified using simulation results.